Research on the Repeater Distribution Based on Monte Carlo Method in Wireless Senor Networks

This article builds two models to analysis the two cases of 1,000 and 10,000 simultaneous users. At first, this paper presents two models of repeater distribution in two cases of 1,000 and 10,000 simultaneous users the minimum numbers of repeaters are 9 and 83 under our assumptions. The repeater distribution problem is transformed to minimum cover problem and Monte Carlo method is employed. Solution of situation with mountain area is discussed. In first model for the case of 1,000 simultaneous users, we apply the theory of "circles covering circles". Unfortunately, we can prove that there are repeaters whose loads are beyond their capacity if we use the theory directly. Instead of trying to find more circles to cover the area, we modify the theory to fit our requirement. In second model for the case of 10,000 simultaneous users, we noticed the fact that hexagon is considered to be the optimal graphic which uses the least nodes to cover the maximum area. In this case, we model the repeater cover regions by several regular hexagons. The key point in this case is to calculate the area of intersection. Recognized the complexity of direct calculation, we follow the idea of the Monte Carlo method.